derivative (ln(x)-1)/(ln^2(x))

解答

导数

\frac{ln ( x ) - 1}{ln ^{2} ( x )}

\frac{- ln ( x ) + 2}{x ln ^{3} ( x )}

求解步骤

\frac{d}{d x} (\frac{ln ( x ) - 1}{ln ^{2} ( x )})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) - 1 ) ln ^{2} ( x ) - \frac{d}{d x} ( ln ^{2} ( x ) ) ( ln ( x ) - 1 )}{( ln ^{2} ( x ) ) ^{2}}

\frac{d}{d x} (ln (x) - 1) = \frac{1}{x}

\frac{d}{d x} (ln^{2} (x)) = \frac{2 ln ( x )}{x}

= \frac{\frac{1}{x} ln ^{2} ( x ) - \frac{2 l n ( x )}{x} ( ln ( x ) - 1 )}{( ln ^{2} ( x ) ) ^{2}}

化简

\frac{\frac{1}{x} ln ^{2} ( x ) - \frac{2 l n ( x )}{x} ( ln ( x ) - 1 )}{( ln ^{2} ( x ) ) ^{2}} : \frac{- ln ( x ) + 2}{x ln ^{3} ( x )}

= \frac{- ln ( x ) + 2}{x ln ^{3} ( x )}

\int sin^{2} (5 θ) d θ

\int \frac{x ^{2} - 5 x + 3}{x - 7} d x

x^{2} + y^{2} = x y y^{^{'}}

in v erse l a pl a ce e^{- 2 s} (\frac{1}{4 s})

\int x (4 - x^{2})^{\frac{1}{2}} d x